PARTICLE PROPERTIES
OF WAVE
Reference:
◆ Beiser Ch 2.1 ~ 2.7
◆ Resnick Ch 1
Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Contents
◼ Electromagnetic waves
◼ Blackbody radiation
◼ Photoelectric effect
◼ Light and X-rays
◼ Compton effect
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Electromagnetic Waves
◼ In classical physics, particles and waves are two different concepts;
however, in modern physics, they are intertwined.
◼ Particles: specific position, mass, energy, momentum, etc.
◼ Waves: wavelength, frequency, power, diffraction, interference,
polarization, etc.
Particle
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Wave
Electromagnetic Waves
◼ EM wave theory:
➢ accelerated electric charges generate linked electric (E) and
magnetic (M) fields; if charges oscillate periodically, E and M fields
are perpendicular to each other and normal to propagation
direction.
➢ A changing M (E) field creates a current before Maxwell; he then
proposed a changing E (M) field creates a M (E) field. Both fields
1
move with light speed 𝑐 = 𝜀 𝜇 = 2.998 × 108 m/s and he
0 0
concluded that light consists of EM waves.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Electromagnetic Waves
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Electromagnetic Waves
◼ In 1888, Hertz showed that EM wave exists
◼ Light is NOT the only EM wave. Its range is 4.3 × 1014 𝑟𝑒𝑑 ~7.5 ×
1014 (𝑣𝑖𝑜𝑙𝑒𝑡).
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Electromagnetic Waves
◼ Principle of superposition:
When two or more waves of the same nature travel past a point at
the same time, the instantaneous amplitude there is the sum of the
instantaneous amplitudes of the individual waves.
◼ Interference:
6
➢
Constructive (in phase) vs. Destructive (pout of phase, partially or
completely)
➢
If two waves have two different frequencies, the result will be a mixture of
constructive and destructive interference.
Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Electromagnetic Waves
◼ Diffraction:
➢ Young’s double part slit experiment
in 1801.
➢ Destructive interference occurs at
half  (/2, 3/2, 5, …) places.
➢ Constructive interference occurs at
integral  (, 3, 5, …) places.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Blackbody Radiation
◼ Birthday of quantum physics: 12/14/1900 as Max Planck
published a conference paper in German physics society
meeting.
◼ As c (light speed) characterizes Einstein’s relativity theory, h
(Planck constant)represents the quantum physics.
◼ Thermal radiation:
➢ Radiation emitted by a body due to the non-zero temperature is
called thermal radiation
➢ All bodies emit and absorb radiation, depending on the
temperature difference between the objects and the environment.
➢ Condensed matters (solid or liquids) emit a continuous spectrum
of radiation, which is independent of its constituents, but on
temperature.
➢ In general, you can see an object because of the reflected light
not the emitted radiation. At higher temperatures, one can see
the radiation (light) emitted from an object.
➢ A blackbody absorbs light shining on it and the emitted radiation
can be observed with the interference from reflected light.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Blackbody Radiation
Blackbody
◼ Spectral radiancy:
𝑅𝑇 𝜈 𝑑𝜈: watt/area per frequency at T
∞
𝑅 = ‫׬‬0 𝑅𝑇 𝜈 𝑑𝜈 = 𝜎𝑇 4 : total power (unit: watt/area) Stefan’s law
𝜎 = 5.67 × 10−8 W/m2-K4 : Stefan-Boltzmann constant
◼ As T increases, the frequency for the maximum radiancy
increases, too (called Wien’s displacement law: 𝜈𝑚𝑎𝑥 ∝ 𝑇)
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Blackbody Radiation
◼ Classical theory of cavity radiation:
➢ Radiation inside a cavity exists in the form of standing wave
➢ Averaged total energy depends on T
➢ Energy density 𝜌𝑇 𝜈 ∝ 𝑅𝑇 𝜈
➢ E field:
𝐸𝑥 𝑥, 𝑡 = 𝐸𝑥0 sin
𝐸𝑦 𝑦, 𝑡 = 𝐸𝑦0 sin
𝐸𝑧 𝑧, 𝑡 = 𝐸𝑧0 sin
2𝜋𝑥
𝜆
2𝜋𝑦
𝜆
2𝜋𝑧
𝜆
sin 2𝜋𝜈𝑡
sin 2𝜋𝜈𝑡
sin 2𝜋𝜈𝑡
➢ Boundary conditions:
𝐸𝑥 0, 𝑡 = 𝐸𝑦 0, 𝑡 = 𝐸𝑧 0, 𝑡 = 0
𝐸𝑥 𝑎, 𝑡 = 𝐸𝑦 𝑎, 𝑡 = 𝐸𝑧 𝑎, 𝑡 = 0
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Blackbody Radiation
𝒏𝒛
𝒏
𝒏𝒚
𝒏𝒙
2𝜋𝑎
𝐸𝑥,𝑦,𝑧 𝑎, 𝑡 = 0 ⟹ 𝜆
𝑥,𝑦,𝑧
= 𝑛𝑥,𝑦,𝑧 𝜋, 𝜈 = 𝜆
𝑐
𝑥,𝑦,𝑧
=
𝑐𝑛𝑥,𝑦,𝑧
2𝑎
, and 𝑛𝑥,𝑦,𝑧 =
2𝑎
𝜈
𝑐
(𝑛𝑥,𝑦,𝑧 : 1, 2, 3, …)
➢ Now assume in the 𝑛 3D space, the number of all radiation
volume
2
4π𝑛2 𝑑𝑛 4π 2𝑎
2𝑎
8π𝑎3 2
2
=
𝜈 ×2×
𝑑𝜈 = 3 𝜈 𝑑𝜈
8
8
𝑐
𝑐
𝑐
polarization
1/8 of space (only positive counted, since 𝑛𝑥,𝑦,𝑧 > 0)
➢ Energy density (J/frequency) is now written as:
𝜌𝑇 𝜈 𝑑𝜈 = 𝐸𝑎𝑣𝑒
energy
11
8π𝑎3 2 1
𝜈 𝑉 𝑑𝜈
𝑐3
total #/volumn
Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
8π
= 𝑘𝐵 𝑇 𝑐 3 𝜈 2 𝑑𝜈 (Rayleigh-Jeans formula)
Blackbody Radiation
𝑒 −𝐸/𝑘𝐵 𝑇
𝑘𝐵 𝑇
𝐸
◼ Quantum theory of cavity radiation (Planck’s theory):
➢ Clearly, at low frequencies, Rayleigh-Jeans formula works well:
𝐸𝑎𝑣𝑒
= 𝑘𝐵 𝑇
Boltzmann distribution
𝜈→0
P(E): energy probability
➢ How to get 𝑘 𝑇?
𝐵
𝐸𝑎𝑣𝑒 =
∞
‫׬‬0 𝐸𝑃 𝐸 𝑑𝐸
∞
‫׬‬0 𝑃 𝐸 𝑑𝐸
𝑒−𝐸/𝑘𝐵 𝑇
𝑘𝐵 𝑇
−𝐸/𝑘
𝐵𝑇
∞𝑒
∞
=
‫׬‬0 𝐸
‫׬‬0
𝑘𝐵 𝑇
𝑑𝐸
𝑑𝐸
= 𝑘𝐵 𝑇
➢ Max Planck used lucky guesswork to have
𝜌𝑇 𝜈 𝑑𝜈 =
12
8𝜋ℎ
𝜈3
𝑑𝜈
𝑐 3 𝑒 ℎ𝜈/𝑘𝐵 𝑇 −1
Solid State Electronics (2024 Spring) by Prof. Jiun-Yun Li
, where ℎ = 6.626 × 10−34 (J-s)
Blackbody Radiation
➢ At high frequencies, the observation shows 𝐸𝑎𝑣𝑒
𝜈→∞
0
➢ So Planck thought 𝐸𝑎𝑣𝑒 is NOT constant, but related to frequency 𝜈. He
assumed 𝐸 = 0, ∆𝐸, 2∆𝐸, 3∆𝐸, …
➢ As ∆𝐸 is small, 𝐸𝑎𝑣𝑒 = 𝑘𝐵 𝑇, just like integration over all E with a very small ∆𝐸;
as ∆𝐸 is large, 𝐸𝑎𝑣𝑒 = 0. So numerically he picked ∆𝐸 ∝ 𝜈 and write down
∆𝐸 = ℎ𝜈, where ℎ = 6.626 × 10−34 (Joule-sec)
𝐸𝑎𝑣𝑒
➢ At low frequencies:
𝜌𝑇 𝜈 𝑑𝜈 =
8𝜋𝜈2
ℎ𝜈
𝑑𝜈
𝑐 3 𝑒 ℎ𝜈/𝑘𝐵 𝑇 −1
=
8𝜋𝜈2
ℎ𝜈
𝑑𝜈
𝑐 3 1+ℎ𝜈/𝑘𝐵 𝑇−1
➢ At high frequencies: 𝜌𝑇 𝜈 𝑑𝜈 → 0
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Solid State Electronics (2024 Spring) by Prof. Jiun-Yun Li
8π
= 𝑘𝐵 𝑇 𝑐 3 𝜈 2 𝑑𝜈
equal to RayleighJeans formula
Blackbody Radiation
◼ If ∆𝐸 ≪ 𝑘𝑇 (or ~ 0) ,
⟹ 𝐸𝑎𝑣𝑒 = 𝑘𝑇
◼ If ∆𝐸 ~ 𝑘𝑇,
⟹ 𝐸𝑎𝑣𝑒 < 𝑘𝑇
◼ If ∆𝐸 ≫ 𝑘𝑇,
⟹ 𝐸𝑎𝑣𝑒 ≪ 𝑘𝑇
◼ So Planck thought ∆𝐸 ∝ 𝜈
➢ At low 𝜈:
✓ Rayleigh/Jean used 𝐸𝑎𝑣𝑒 = 𝑘𝑇 to get
8π
𝑘𝐵 𝑇 3 𝜈 2 ;
𝑐
✓ Planck assumed 𝐸 = ℎ𝜈 (small), got it, too!
➢ At high 𝜈:
✓ Rayleigh/Jean failed
✓ Planck assumed 𝐸 = ℎ𝜈 (large), he got
𝐸𝑎𝑣𝑒 → 0, matching the experimental
results
✓ Actual form of 𝐸𝑎𝑣𝑒 =
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
ℎ𝜈
𝑒 ℎ𝜈/𝑘𝐵 𝑇 −1
Blackbody Radiation
◼ Example (Planck’s theory): derive Planck’s expression for 𝐸𝑎𝑣𝑒 =
ℎ𝜈
𝑒 ℎ𝜈/𝑘𝐵 𝑇 −1
𝒆−𝑬/𝒌𝑩 𝑻
𝑷 𝑬 =
𝒌𝑩 𝑻
◼ Solutions:
➢
𝑑
−𝑦 𝑑𝑦 ln
➢ 𝐸𝑎𝑣𝑒 =
−𝑛𝑦
σ∞
𝑛=0 𝑒
σ∞
𝑛=0 𝐸𝑃(𝐸)
σ∞
𝑛=0 𝑃(𝐸)
=
𝑬𝒏 = 𝒏𝒉𝝂
=
−𝑦
𝑑 ∞
σ
𝑒 −𝑛𝑦
𝑑𝑦 𝑛=0
−𝑛𝑦
σ∞
𝑛=0 𝑒
𝑒−𝑛ℎ𝜈/𝑘𝐵 𝑇
σ∞
𝑛=0 𝑛ℎ𝜈
𝑘𝐵 𝑇
𝑒−𝑛ℎ𝜈/𝑘𝐵 𝑇
σ∞
𝑛=0
𝑘𝐵 𝑇
𝑑
=
=
𝑑 −𝑛𝑦
𝑒
𝑑𝑦
𝑒 −𝑛𝑦
− σ∞
𝑛=0 𝑦
σ∞
𝑛=0
=
−𝑛𝑦
σ∞
𝑛=0 𝑛𝑦𝑒
𝑘𝐵 𝑇 σ∞ 𝑒 −𝑛𝑦
𝑛=0
𝑑
−𝑛𝑦
σ∞
𝑛=0 𝑛𝑦𝑒
−𝑛𝑦
σ∞
𝑛=0 𝑒
−𝑛𝑦 = −ℎ𝜈
−𝑦 + 𝑒 −2𝑦 + ⋯
= −𝑘𝐵 𝑇𝑦 𝑑𝑦 ln σ∞
ln
1
+
𝑒
𝑛=0 𝑒
𝑑𝑦
𝑑
= −ℎ𝜈 𝑑𝑦 ln
=
𝑒 −𝑦
ℎ𝜈 1−𝑒 −𝑦
1
1−𝑒 −𝑦
= ℎ𝜈 1 − 𝑒 −𝑦 𝑒 −𝑦
1
= ℎ𝜈 𝑒 𝑦 −1 = ℎ𝜈
1
(1−𝑒 −𝑦 )2
1
ℎ𝜈
𝑘
𝑒 𝐵𝑇
−1
◼ Oscillator energies: 𝐸𝑛 = 𝑛ℎ𝜈, n = 0, 1, 2, …
◼ Average energy per oscillator (or standing wave):
1
𝐸𝑎𝑣𝑒 = ℎ𝜈 ℎ𝜈
𝑒 𝑘𝐵 𝑇 − 1
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
ℎ𝜈
𝐵𝑇
,𝑦=𝑘
Blackbody Radiation
𝜈 is too small for the quantization of energy
to be observed (or say 𝜆 is too long)
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Blackbody Radiation
Father of Quantum!
But only got Nobel in 1918
(so late, why?)
Rayleigh still got Nobel in 1904!
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
The energies of electrons liberated by light depend on the
frequency of the light
◼ Backgrounds:
➢ Hertz confirmed the existence of EM wave. He also found
there are some sparks in his experiment (but did not think
deeper to see that’s the evidence of photoelectric effects)
➢ However, his experiment was often used to contradict EM
wave theory, that says EM wave is also particles.
➢ Leonard following Hallwachs did show that those incident
light can eject the electrons (which was later explained by
Einstein).
➢ Einstein got his first and ONLY Nobel prize in Physics for
proposing a theory of photoelectric effects (i.e. quantum
theory of light) which states the particle properties of wave.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
◼ Experiment
➢ An evacuated tube (vacuum tube) to avoid air particles
➢ Light is impinging on the metal electrode surfaces. Some
electrons gaining energy from light (EM wave) and leave the
surface.
➢ Then a potential drop applied to provide an E field to collect
electrons by connected with a current meter.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
◼ Concerns:
➢ No time lag between light arrival (impinging) and the generated electrons (or
say at least < 1 ns)
➢ Retarding potential: the required potential to generate the E field to
decelerate the ejected electrons by light
➢ For light of different intensities (W/m2), how come the retarding potential is
the same? EM wave can deliver the energy to any object such that
electrons in the electrodes eventually collect enough energy to be ejected.
➢ If light with a higher frequency, photocurrent is higher; furthermore, no
matter what the frequency is, its retarding potential is zero, photocurrent is
the same. Why?
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
◼ Explanation (Light is a particle!)
➢ No need to accumulate energy from “light wave”
➢ So no matter how high the light intensity is, a “light particle” has the
same energy (at a constant frequency) such that an ejected electron
can only absorb maximum energy of a “light particle” determined by 𝜈.
➢ Then retarding potential corresponds to the maximum energy of a
single “light particle”.
➢ Larger light intensities mean “more” light particles.
➢ Since a “light particle” with a higher frequency means it has higher
energy, the retarding potential is larger.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
➢ The so-called light particles are photons (named by Gilbert Lewis and
theory by Einstein).
◼ Quantum theory of light:
➢ Photon energy:
6.626×10−34
ℎ𝜈 = 6.626 × 10−34 𝜈 𝐻𝑧 = 1.602×10−19 𝜈 = 𝜈4.136 × 10−15 (eV)
=
𝑐
4.136 × 10−15 𝜆
=
1.24×10−6
𝜆 (𝑚)
1.24
(eV) = 𝜆 (𝜇𝑚) (eV)
➢ Work function  ℎ𝜈0 , where 𝜈0 is minimum frequency for electrons to
be ejected from an object surface
➢ ℎ𝜈 = ℎ𝜈0 + 𝐾𝐸𝑚𝑎𝑥
22
→
𝐾𝐸𝑚𝑎𝑥 = ℎ𝜈 − ℎ𝜈0
Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Photoelectric Effects
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
What is Light?
◼ Wave and particle seem against each other,
but photons still need the wave frequency to
represent its energy
◼ Wave vs. Particle is NOT the same as
Newton vs. Relativity (since Newton is an
approximation of Relativity as 𝑣 ≪ 𝑐)
◼ Wave: (𝐸 2 ) vs. Particle (𝑛ℎ𝜈):
➢ Wave stands for probability of finding
photons (quantum mechanics later)
➢ As N is large (or observation period is
long), Particle behavior will be like Wave
(continuous distribution)
➢ Light travels as wave and interact with
media as particles.
➢ Duality will be discussed later
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
◼ Light to particle via photoelectric
effect, what about the inverse process
(particle to light)? Yes, it’s discover
earlier than Planck and Einstein
◼ Roentgen found a highly unknown
radiation as fast electrons impinge on
matters, called X-ray.
➢ unaffected by E and M fields
➢ faster electrons lead to more
penetration
➢ more electrons leads to higher
intensity of X-ray beam
◼ Max von Laue found that
➢ diffraction spacing comparable to atomic space in crystals
➢ X-ray wavelength 0.13 ~ 0.48 Å ; 10−4 shorter than visible light and 104
more energetic
➢ We define 0.1 to 100 Å as X-ray wavelength range
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
Thermionic emission:
Electrons ejected from the
object due to high
temperature
◼ Electron generation: a cathode heated by a filament where electric
current passes. Electrons are provided by thermionic emission.
◼ Electron acceleration: by applying a large E field to accelerate the
emitted electrons from the filament.
◼ Then the accelerated electrons are stopped on the target to
radiate EM waves called bremsstrahlung (braking radiation).
◼ However, theory did not match with experiment results by showing
something that can be explained by classical EM theory.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
◼ Emitted X-ray at a given accelerating potential vary in wavelength; further,
there exists a threshold wavelength (𝜆𝑚𝑖𝑛 ), which is the same for Mo and
W:
𝑒𝑉 − ℎ𝜈0 ≈ 𝑒𝑉 = ℎ𝜈𝑚𝑎𝑥 = 𝜆
ℎ𝑐
𝑚𝑖𝑛
➢
ℎ𝑐
→ 𝜆𝑚𝑖𝑛 = 𝑒𝑉 =
1.24
𝑉
(m)
This can be explained by photoelectric effect and it is the inverse of
photoelectric effect.
◼ By measuring the radiation spectrum of Mo, certain peaks were observed.
(atomic spectrum due to discrete energy levels of electrons in the atom)
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
◼ At 1901, he got first Nobel Physics prize and
was the only one person
◼ Single winner year (
➢ 1904: Rayleigh
➢ 1906: Thomson
➢ 1907: Michelson
➢ 1914: Max von Laue
➢ 1921: Einstein
……..
➢ 1992 Charpak (last single winner)
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
◼ Since the atomic spacing is ~ X-ray wavelength, X-ray impinges into a
crystal will give us some beautiful diffraction patterns
◼ In crystals, as EM wave interact with atoms, there are negatively and
positively charged particles which creates polarized dipoles and thus, E
field. Since AC EM wave alternates, the resulted oscillated dipoles
generate a radiation with the same frequency. Those resulting radiation
is called scatted wave.
◼ What is crystal? Regularly positioned atoms.
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Light and X-Rays
◼ Then scattered wave in the crystals will
constructively or destructively interfere.
◼ Bragg diffraction:
➢ Parallel waves must be in phase (∆𝜃 = 2𝑛𝜋, n =
integers) for constructive interference.
➢ The light path difference makes the phase difference:
2𝜋
𝑘 𝑑sin𝜃 × 2 = 2𝑛𝜋 →
2𝑑sin𝜃 = 2𝑛𝜋 → 2𝑑sin𝜃 = 𝑛𝜆
𝜆
➢ Or you can say light path different must be 𝜆, 2𝜆, 3𝜆, …
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Energy and Momentum in Relativity
◼ Relativity mass: 𝑚 =
◼ Momentum: 𝑝 =
𝑚0
𝑣2
1− 2
𝑐
; 𝑚0 : rest mass (𝑣 = 0)
𝑚0 𝑣
𝑣2
1− 2
𝑐
◼ Total energy: 𝐸 =
𝑚0 𝑐 2
𝑣2
1− 2
𝑐
→
𝐸2
−
𝑝2 𝑐 2
=
𝑚02 𝑐 4
𝑣2
1− 2
𝑐
−
𝑚02 𝑣 2 𝑐 4
𝑣2
1− 2
𝑐
◼ Massless particle (photons): 𝐸 = 𝑝𝑐
◼ Electron volt (energy unit): 1 𝑒𝑉 = 1.6 × 10−19 (J)
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
= (𝑚0 𝑐 2 )2
Compton Effects
◼ Interaction between photons and electrons:
➢ Energy: photon energy loss = electron energy gain: 𝐾𝐸 = ℎ𝜈 − ℎ𝜈 ′
✓ Total energy of a particle: 𝐸 = 𝐾𝐸 + 𝑚𝑐 2 =
(𝑚𝑐 2 )2 +𝑝2 𝑐 2
➢ Momentum:
✓ For a massless particle (photon): 𝑝 =
✓ For a particle with mass: 𝑝 =
𝑚𝑣
𝐸
𝑐
=
ℎ𝜈
𝑐
from 𝐸 =
relativity
(𝑚𝑐 2 )2 +𝑝2 𝑐 2 =
𝑝2 𝑐 2 = 𝑝𝑐
1−𝑣 2 /𝑐 2
✓ Initial momentum = final momentum
0+
ℎ𝜈
𝑐
=
ℎ𝜈′
cos 𝜙
𝑐
+ 𝑝 cos 𝜃 (horizontal);
ℎ𝜈′
sin 𝜙 − 𝑝 sin 𝜃 (vertical)
𝑐
ℎ𝜈
ℎ𝜈′
ℎ𝜈′
𝐾𝐸, 𝑐 = 𝑐 cos 𝜙 + 𝑝 cos 𝜃, and 0 = 𝑐 sin 𝜙
→ 𝑝2 𝑐 2 = (ℎ𝜈)2 −2 ℎ𝜈 ℎ𝜈 ′ cos 𝜙 + (ℎ𝜈′)2
0=
ℎ𝜈 − ℎ𝜈 ′ =
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
− 𝑝 sin 𝜃
Compton Effects
➢ Total energy: 𝐸 = 𝐾𝐸 + 𝑚𝑐 2 = (𝑚𝑐 2 )2 +𝑝2 𝑐 2
→ 𝑝2 𝑐 2 = (ℎ𝜈 − ℎ𝜈 ′ )2 +2𝑚𝑐 2 ℎ𝜈 − ℎ𝜈 ′
= (ℎ𝜈)2 −2 ℎ𝜈 ℎ𝜈 ′ + (ℎ𝜈′)2 +2𝑚𝑐 2 ℎ𝜈 − ℎ𝜈 ′
→ 𝑝2 𝑐 2 = (ℎ𝜈)2 −2 ℎ𝜈 ℎ𝜈 ′ cos 𝜙 + (ℎ𝜈′)2
(from momentum calculation in the previous slide)
➢ Compare the above two 𝑝2 𝑐 2 terms:
2𝑚𝑐 2 ℎ𝜈 − ℎ𝜈 ′ = 2 ℎ𝜈 ℎ𝜈 ′ 1 − cos 𝜙
ℎ
→ ∆𝜆 = 𝜆′ − 𝜆 = 𝑚𝑐 1 − cos 𝜙 = 𝜆𝐶 1 − cos 𝜙
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Compton Effects
35
Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Compton Effects
ℎ
∆𝜆 = 𝜆′ − 𝜆 = 𝑚𝑐 1 − cos 𝜙 = 𝜆𝐶 1 − cos 𝜙
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Compton Effects
◼ He is the 3rd US Nobel Physics prize winner (1st:
Michelson, 1907; 2nd: Millikan, 1923)
◼ US Winners: 94 out of 210 (1901 ~ 2018) ~ 45 %
◼ US Winners: 85 out of 157 (1949 ~ 2018) ~ 54 %
◼ US Winners: 3 out of 36 (1901 ~ 1930) ~ 8 %
◼ Princeton Alumni: 65 in total and 43 did work in or
got degrees from Princeton
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li
Homework
◼ Ch 1: 30, 35
◼ Ch 2: 1, 3, 8, 11, 12, 15, 17, 21, 24, 28, 30, 35
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Modern Physics (2024 Spring) by Prof. Jiun-Yun Li